Test review please help

Question

Answer 1

23).

The matrix and .

To find , first find  then multiply B with it.

Matrix multiplication :

• If the number of columns in the first matrix is equal to the number of rows in second matrix then the multiplication is possible.
• Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.
• Add the products.

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Answer 2

24).

, then.

The matrix is  .

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Answer 3

25).

The reduced row echelon for that results from gauss - jordan riw reduction of a system of linear equations is .

Consider the system as AX = B.

Where, , and .

Rank of matrix A is 2, rank of augmented matrix is 2 and number of unknowns are 3.

Remember that, if rank of A = rank of augmented matrix < number of unknowns then, the system have infinitely many solutions.

x + 3y = 7 and z = 8.

Therefore, the given system has infinitely many solutions.